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Birational geometry of foliations associated to simple derivations and generalizations

Abstract : We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor singularities in the complement of a line. We establish the position of these foliations in the birational classification of foliations and prove the finiteness of their birational symmetries. Most of the results apply to wider classes of foliations.
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Contributor : Gaël Cousin Connect in order to contact the contributor
Submitted on : Friday, January 6, 2017 - 11:48:42 AM
Last modification on : Friday, January 7, 2022 - 11:00:13 AM
Long-term archiving on: : Friday, April 7, 2017 - 1:28:17 PM


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Gaël Cousin, Luis Gustavo Mendes, Ivan Pan. Birational geometry of foliations associated to simple derivations and generalizations. 2017. ⟨hal-01428028⟩



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